1. Field of the Invention
The present invention relates generally to data storage and communication systems, and more particularly to data compression systems and methods which improve the capacity of data storage and communication.
2. Description of the Prior Art
Due to the insignificant differences between data compression in data storage and data communication systems, only data storage systems are referred to; particularly the data files stored in such systems. However, all data storage systems can easily be extended to cover data communications systems and other applications as well. A file is assumed to be a sequential stream of bytes or characters, where a byte consists of some fixed number of bits (typically 8), and the compression system transforms this input byte stream into a "compressed" output stream of bytes from which the original file contents can be reconstructed by a decompression unit.
It is well-established that computer data files typically contain a significant amount of redundancy. Many techniques have been applied over the years to "compress" these files so that they will occupy less space on the disk or tape storage medium or so that they can be transmitted in less time over a communications channel such as a 1200 baud modem line. For example, there are several widely used commercial programs available for personal computers (e.g., ARC Software by Systems Enhancement Associates, Inc., Wayne, N.J., 1985) which perform the compression and decompression functions on files. It is not uncommon for such programs to reduce the size of a given file by a 2:1 ratio (or better), although the amount of reduction varies widely depending on the contents of the file.
There are many approaches in the prior art for compressing data. Some of these approaches make implicit assumptions about certain types of files or data within the files. For example, a bit image of a page produced using a scanner typically has most of its pixels blank, and this tendency can be exploited by a compression algorithm to greatly reduce the size of such files. Similarly, word processing files contain many ASCII characters which are easily compressed using knowledge of which characters (or words) occur most frequently in the language of interest (e.g., English). Other compression methods are independent of the file type and attempt to "adapt" themselves to the data. In general, type-specific compression techniques may provide higher compression performance than general-purpose algorithms on the file for which the techniques are optimized, however they tend to have much lower compression performance if the file model is not correct. For instance, a compression method optimized for English text might work poorly on files containing French text.
Typically, a storage system does not "know" what type of data is stored within it. Thus, data-specific compression techniques are avoided, or they are only used as one of a set of possible techniques. For example, ARC uses many methods and picks the one that performs best for each file; note however that this approach requires significant computational overhead compared to using a single compression method.
Another important aspect of any compression method is the speed at which a file can be processed. If the speed of compression (or decompression) is so low as to significantly degrade system performance, then the compression method is unacceptable even though it may achieve higher compression ratios than competing methods. For example, with streaming tape systems, if the file cannot be compressed fast enough to provide data at the required rate for the tape drive, the tape will fall out of streaming and the performance and/or capacity gains due to compression will be nullified.
One of the most common compression techniques is known as run-length encoding. This approach takes advantage of the fact that files often have repeated strings of the same byte (character), such as zero or the space character. Such strings are encoded using an "escape" character, followed by the repeat count, followed by the character to be repeated. All other characters which do not occur in runs are encoded by placing them as "plain text" into the output stream. The escape character is chosen to be a seldom used byte, and its occurrence in the input stream is encoded as a run of length one with the escape character itself as the character. Run-length encoding performs well on certain types of files, but can have poor compression ratios if the file does not have repeated characters (or if the escape character occurs frequently in the file). Thus, the selection of the escape character in general requires an extra pass on the data to find the least used byte, lowering the throughput of such a system.
A more sophisticated approach is known as Huffman encoding (see, Huffman, David A., "A Method for the Construction of Minimum-Redundancy Codes", Proceedings of the IRE, pp. 1098-1110, September 1952). In this method, it is assumed that certain bytes occur more frequently in the file than others. For example, in English text the letter "t" or "T" is much more frequent than the letter "Q". Each byte is assigned a bit string, the length of which is inversely related to the relative frequency of that byte in the file. These bit strings are chosen to be uniquely decodeable if processed one bit at a time. Huffman derived an algorithm for optimally assigning the bit strings based on relative frequency statistics for the file.
The Huffman algorithm guarantees that asymptotically the compression achieved will approach the "entropy" of the file, which is precisely defined as, ##EQU1##
The units of H are in bits, and it measures how many bits (on the average) are required to represent a character in the file. For example, if the entropy were 4.0 bits using an 8-bit byte, a Huffman compression system could achieve 2:1 compression on the file. The higher the entropy, the more "random" (and thus less compressible) is the data.
Huffman encoding works very well on many types of files. However, assignment of bit strings to bytes presents many practical difficulties. For example, if a pre-assigned encoding scheme is used (e.g., based on frequency of occurrence of letters in English), Huffman encoding may greatly expand a file if the pre-assigned scheme assumes considerably different frequency statistics than are actually present in the file. Additionally, computing the encoding scheme based on the file contents not only requires two passes over the data as well as applying the Huffman algorithm to the frequency statistics (thus lowering system throughput), but it also requires that the encoding table be stored along with the data, which has a negative impact on the compression ratio. Furthermore, the relative frequency of bytes can easily change dynamically within the file, so that at any point the particular encoding assignment may perform poorly.
There have been many variations on the Huffman approach (e.g., Jones, Douglas W., "Application of Splay Trees to Data Compression", Communications of the ACM, pp. 996-1007, Vol. 31, No. 8, August 1988) and they usually involve dynamic code assignment based on the recent history of input bytes processed. Such schemes circumvent the problems discussed above. Other approaches include looking at two byte words (bi-grams) at the same time and performing Huffman encoding on the words.
A recent variation of Huffman encoding is present in U.S. Pat. No. 4,730,348 to MacCrisken (and other patents referenced therein). In MacCrisken, Huffman codes are assigned to bytes in the context of the previous byte. In other words, a plurality of encoding tables are used, each table being selected according to the previous byte. This approach is based on the observation that, for example, in English the letter "u" does not occur very frequently, but following a "q" it appears almost always. Thus, the code assigned to "u" would be different depending on whether or not the previous letter was "q" (or "Q"). For a similar scheme using multiple tables and dynamic code assignment see, Jones, Douglas W., "Application of Splay Trees to Data Compression".
The above described Huffman-type approaches tend to be computationally intensive and do not exceptionally achieve high compression ratios. One explanation for this observation is that a pure Huffman code based on 8-bit bytes can achieve at best an 8:1 compression ratio, and only in the optimal situation when the file consists of the same byte repeated over and over (i.e. entropy=0). In the same scenario a simple run-length encoding scheme could achieve better than a 50:1 compression ratio. The average performance will be some combination of best and worst case numbers, and limiting the best case must also limit the average. An ideal Huffman code should be able to use "fractional" bits to optimize code assignment, but the practical limitation of integral numbers of bits in each code limits the Huffman performance to well below its theoretical limit. A totally different approach to compression was developed by Ziv and Lempel (see, Ziv, J. and Lempel, A., "Compression of Individual Sequence via Variable Rate coding", IEEE Transactions on Information Theory, Vol. IT-24, pp. 530-536, September 1978) and then refined by Welch (see, Welch, Terry A., "A Technique for High-Performance Data Compression", IEEE Computer, pp. 8-19, June 1984). Instead of assigning variable length codes to fixed size bytes, the Liv-Lempel algorithm ("ZL") assigns fixed-length codes to variable size strings. As input bytes from the file are processed, a table of strings is built up, and each byte or string of bytes is compressed by outputting only the index of the string in the table. Typically this index is in the range 11-14 bits, and 12 bits is a common number because it lends itself to a simple implementation. Since the table is constructed using only previously encoded bytes, both the compression and the decompression system can maintain the same table without any extra overhead required to transmit table information. Hashing algorithms are used to find matching strings efficiently. At the start of the file, the table is initialized to one string for each character in the alphabet, thus ensuring that all bytes will be found in at least one string, even if that string only has length one.
The Ziv-Lempel algorithm is particularly attractive because it adapts itself to the data and requires no pre-assigned tables predicated on the file contents. Furthermore, since a string can be extremely long, the best case compression ratio is very high, and in practice ZL out performs Huffman schemes on most file types. It is also quite simple to implement, and this simplicity manifests itself in high throughput rates. There are also some drawbacks, however, to the ZL compression method. The ZL string search is a "greedy" algorithm. For example, consider the string: EQU ABCDEFBCDEF;
where A,B,C,D,E,F are any distinct bytes. Note that the ZL string search would add the following strings to its string table: AB, BC, CD, DE, EF, BCD, DEF, the only strings of length two or greater that can be output using this algorithm, up to the point shown, are BC and DE. In actuality the string BCDEF has already occurred in the input. Thus, while ideally the second BCDEF string would be referenced back to the original BCDEF, in practice this does not occur.
A more significant disadvantage to the ZL approach is that the string table for holding the compressed data will tend to fill up on long files. The table size could be increased, however, this approach would require more bits to represent a string and thus it would be less efficient. One approach to handling this deficiency would be to discard all or part of the table when it fills. Because of the structure of the algorithm, the most recently found strings have to be discarded first, since they refer back to previous strings. However, it is the most recent strings that have been dynamically adapting to the local data, so discarding them is also inefficient. Basically, the ZL string table has infinite length memory, so changes in the type of data within the file can cause great encoding inefficiencies if the string table is full.
It is also possible to design a compression system that utilizes more than one method simultaneously, dynamically switching back and forth depending on which method is most efficient within the file. From an implementation standpoint, such a scheme may be very costly (i.e., slow and/or expensive), however the resulting compression rate could be very high.
One such method of dynamically switching back and forth is disclosed in MacCrisken. As mentioned above, a bi-gram Huffman method is utilized as the primary compression technique. Typically the compression and decompression system start with a pre-defined (i.e. static) set of code tables. There may be a set of such tables, perhaps one each for English, French, and Pascal source code. The compression unit (sender) first transmits or stores a brief description of which table is to be used. The decompression unit (receiver) interprets this code and selects the appropriate table. During compression, if it is determined that the current table not performing well, the sender transmits a special ("escape") Huffman code that tells the receiver to either select another specific pre-defined table or to compute a new table based on the previous data it has decompressed. Both sender and receiver compute the table using the same algorithm, so there is no need to send the entire table, although it takes some time to perform the computation. Once the new table is computed, compression proceeds as before. It should be noted that although there is considerable computational overhead, there is no reason why this technique could not be further adapted to a dynamic Huffman scheme.
In addition to the Huffman encoding, MacCrisken used a secondary string-based compression method. Both sender and receiver maintain a history buffer of the most recently transmitted input bytes. For each new input byte (A), the bi-gram Huffman code is generated, but an attempt is also made to find the string represented by the next three input bytes (ABC) in the history using a hashing scheme. The hash is performed on three byte strings and a doubly-linked hash list is maintained to allow discarding of old entries in the hash list. If a string is found, a special Huffman escape code can be generated to indicate that a string follows, and the length and offset of the string in the history buffer is sent. The offset is encoded in 10 bits, while the length is encoded into 4 bits, representing lengths from 3-18 bytes. Before such a string is sent however, the compression unit generates the Huffman codes for all the bytes in the string and compares the size of the Huffman codes with the size of the string bits. Typically the Huffman string escape code is four bits, so it takes 19 bits to represent a string. The smaller of the two quantities is sent.
Note that the MacCrisken string method avoids the problems of the Ziv-Lempel method in that the string "table" never fills up, since the old entries are discarded by removing them from the hash list. Thus, only the most recent (within 1K bytes) strings occupy the table. Also it is not "greedy" since in principle all matching strings can be found. In practice, a limit on the length of the string search is imposed. Additionally, the MacCriskin method is computationally inefficient because it is effectively performing two compression algorithms at once, and thus the computational overhead is quite high.